NEW YORK (CNNMoney.com) -- The Obama administration gave General Motors and Chrysler LLC failing grades Monday for their turnaround efforts and promised a sweeping overhaul of the troubled companies. The government plans to give the automakers more money, but it is also holding out the threat of a "structured bankruptcy."

The federal government will provide operating funds for both automakers for several weeks, during which time the companies will have to undergo significant restructuring, administration officials said late Sunday night.

At GM, part of that restructuring began early Monday when CEO Rick Wagoner announced his resignation, which he said came at the request of the Obama administration.

President Obama said Monday that the government would try to help the companies, which have already been given $17.4 billion, survive.

"We cannot, we must not, and we will not let our auto industry simply vanish," Obama said from the White House. "This industry is, like no other, an emblem of the American spirit; a once and future symbol of America's success."

GM (GM, Fortune 500) will get 60 days and Chrysler 30 days in which to make a final push toward proving they can run viable businesses. If Chrysler succeeds, it will receive a $6 billion loan. In GM's case, the officials would not specify how much money the carmaker might receive.

In the case of both companies, the officials said, stakeholders - and particularly debt holders in both companies - had not done enough to relieve the automakers of ongoing financial burdens.

"We have made very clear that we expect a very, very substantial reduction in liability for both companies," one official said.

The administration also said a structured bankruptcy is possible.

"While Chrysler and GM are different companies with different paths forward, both have unsustainable liabilities and both need a fresh start," according to an administration document. "Their best chance at success may well require utilizing the bankruptcy code in a quick and surgical way."

In order to help assuage consumer fears about buying cars from these companies as they restructure, the government is also setting aside funds to back up warranties on vehicles GM and Chrysler sell.

GM: Changes at the top

The administration officials were far more positive in their tone regarding the prospects for GM than for its smaller rival.

"We are very confident GM can survive and thrive as a company," one official said, noting the company's global reach, the strength of its research and development and the power of its various brands.

Nevertheless, significant changes are on the table.

One was the resignation of chief executive Wagoner, a 32-year veteran of the company who has served in the top post since 2000.

"On Friday I was in Washington for a meeting with administration officials. In the course of that meeting, they requested that I 'step aside' as CEO of GM, and so I have," Wagoner said in a statement posted to the GM Web site.

"Having worked closely with Fritz for many years, I know that he is the ideal person to lead the company through the completion of our restructuring efforts. His knowledge of the global industry and the company are exceptional, and he has the intellect, energy, and support among GM'ers worldwide to succeed," Wagoner said.

"We view our approach to GM as starting with a clean sheet of paper," the Treasury official said.

The officials said they had committed to working with GM to create a leaner, more competitive company. Administration officials will be in Detroit working very closely with the GM executives on a plan to restructure the company and its debt obligations, the officials said.

"We have significant challenges ahead of us, and a very tight timeline," Henderson said in a prepared statement released Monday. "I am confident that the GM team will succeed, and that a stronger, healthier GM will play an important role in revitalizing America's economy and re-establishing its technology leadership and energy independence."

The administration officials would not say how much more money they might ultimately lend to GM or how much working capital the automaker would need to make it through the next 60 days.

Chrysler: Fiat or bust

For its part, Chrysler was too reliant on the domestic auto market, according to the officials. In addition, a significant "hollowing out" of the company by its past owners had left it unable to compete effectively as a stand-alone company, the officials said.

Any restructuring for Chrysler would have to involve a partnership, most likely a deal with Fiat which has had an "agreement in principal" with Chrysler since January.

Chrysler is getting 30 days to work out a deal with Fiat, which is the only way the officials believe the carmaker will survive. If that can happen, the administration is prepared to lend Chrysler $6 billion dollars more.

While government officials said it was their "goal, hope and ambition" for a Chrysler-Fiat deal to work, the agreement terms would need to be modified from what the companies had previously announced.

Fiat had originally planned to take a 35% stake in Chrysler, but that stake would have to be lower. Fiat would also not be allowed to own a majority stake in Chrysler until after all government loans have been repaid.

"We are pleased that Chrysler, Fiat and Cerberus have reached agreement on a framework of a global alliance, supported by the U.S. Treasury," Chrysler spokeswoman Shawn Morgan said in statement released Monday. "Chrysler has consistently said that the alliance with Fiat enhances its business model that expands its global competitiveness." Morgan emphasized that discussions on a deal wit Fiat are still ongoing.

There is sufficient money in existing funds to finance these plans, the officials said, who added that there would be no immediate need to ask Congress to appropriate more.